Determining component contributions of time-series model

ABSTRACT

Provided is a system and method which decomposes a predicted output signal of a time-series forecasting model into a plurality of sub signals that correspond to a plurality of components, and determines and displays a global contribution of each component. In one example, the method may include iteratively predicting an output signal of a time-series data value via execution of a time-series model, decomposing the predicted output signal into a plurality of component signals corresponding to a plurality of components of the time-series machine learning algorithm, respectively, and displaying the plurality of global values via a user interface.

BACKGROUND

Time-series data contains sequential data points (e.g., data values)that are observed at successive time durations (e.g., hourly, daily,weekly, monthly, annually, etc.). For example, monthly rainfall, dailystock prices, annual profits, etc., are examples of time-series data.Forecasting is a machine learning process which can be used to observehistorical values of time-series data and predict future values of thetime-series data. There are numerous types of forecasting modelsincluding exponential smoothing which uses a weighted sum of pastobservations of the time-series to make predictions about future valuesof the data.

A predicted time-series value may be graphed as a plurality of datapoints over time and displayed on a user interface for an analyst orother user to visualize and possibly take actions according to theprediction. However, the graph by itself does not provide an analystwith an adequate understanding of what factors, within the model, arecontributing to the predicted output value. Therefore, an analyst mayhave a difficult time understanding and interpreting the results outputfrom the time-series forecasting model.

BRIEF DESCRIPTION OF THE DRAWINGS

Features and advantages of the example embodiments, and the manner inwhich the same are accomplished, will become more readily apparent withreference to the following detailed description taken in conjunctionwith the accompanying drawings.

FIG. 1 is a diagram illustrating a process of executing a machinelearning model and a decomposition application in accordance with anexample embodiment.

FIG. 2A is a diagram illustrating a predicted output signal of atime-series forecasting model in accordance with an example embodiment.

FIG. 2B is a diagram illustrating different component signals includedin the predicted output signal of FIG. 1, in accordance with an exampleembodiment.

FIG. 3A is a diagram illustrating a graph displaying different componentsignals of a time-series forecasting model in accordance with an exampleembodiment.

FIG. 3B is a diagram illustrating a process of displaying global impactvalues of the different component signals of the time-series forecastingmodel in accordance with an example embodiment.

FIG. 4A is a diagram illustrating a process of generating adecomposition table for global contribution value determination inaccordance with example embodiments.

FIG. 4B is a diagram illustrating a process of determiningmulti-dimensional global contribution values for the plurality ofcomponent signals in accordance with an example embodiment.

FIG. 5 is a diagram illustrating a method of determining contributionvalues of a plurality of components of a time-series forecasting modelin accordance with an example embodiment.

FIG. 6 is a diagram illustrating a computing system for use in theexamples herein in accordance with an example embodiment.

Throughout the drawings and the detailed description, unless otherwisedescribed, the same drawing reference numerals will be understood torefer to the same elements, features, and structures. The relative sizeand depiction of these elements may be exaggerated or adjusted forclarity, illustration, and/or convenience.

DETAILED DESCRIPTION

In the following description, specific details are set forth in order toprovide a thorough understanding of the various example embodiments. Itshould be appreciated that various modifications to the embodiments willbe readily apparent to those skilled in the art, and the genericprinciples defined herein may be applied to other embodiments andapplications without departing from the spirit and scope of thedisclosure. Moreover, in the following description, numerous details areset forth for the purpose of explanation. However, one of ordinary skillin the art should understand that embodiments may be practiced withoutthe use of these specific details. In other instances, well-knownstructures and processes are not shown or described in order not toobscure the description with unnecessary detail. Thus, the presentdisclosure is not intended to be limited to the embodiments shown but isto be accorded the widest scope consistent with the principles andfeatures disclosed herein.

Time-series forecasting models are used to predict a single set ofvalues of an item (e.g., cost, quantity, amount, intensity, etc.)recorded over equal time increments (e.g., minutes, days, hours, weeks,years, etc.) The models may support data properties that are frequentlyfound in business applications such as trends, seasonality,fluctuations, residuals, and time dependence. Model features may betrained based on available historical data. The trained model can thenbe used to forecast future values for the data. Some examples oftime-series forecasting models include exponential smoothing (ETS) andautoregressive integrated moving average (ARIMA) just to name a few.

A business analyst may build a time-series forecasting function for aperiod of time referred to as a horizon (h). The horizon may include aplurality of equal time increments with each increment being referred toas a unit of the horizon. For example, if a predictive model predictsthe changes to sales of apples on a day-by-day basis, the horizon may bea week, with the time increments being individual days. In many cases,the prediction generated by the forecasting model may include a numberof sequential horizons.

Decomposition refers to a process of decomposing a time-seriesforecasting model to understand how the time-series forecasting modelhas been built. The decomposition can be either additive ormultiplicative. For additive decomposition, the contribution of eachmodel component can be merely added up to obtain the final predictionvalue at each time increment. For example, an iteration of a time-seriesforecasting model may be graphed as a data point on a graph with thepredicted value arranged on one axis of the graph (e.g., the y axis) andincrements of time being arranged on the other axis (e.g., the x axis).This data point may be decomposed into a plurality of sub data pointsthat represent different components of the time-series forecasting modelincluding a trend component, a cyclical component (e.g., seasonality), aresidual component, an influencer component, etc. at that increment oftime. However, these components in their respective visualrepresentation are often at significantly different scales with respectto each other. As a non-limiting example, a trend component may have avalue that varies between −0.15 and 0.2 as it represents the slope ofthe signal variation per time unit while an influencer component mayhave a value that varies between −2000 and 2000 in the signal unit. Thismakes it difficult to compare the effects that each component has on theoverall predicted output signal.

The example embodiments are directed to a decomposition process andsystem which can identify and visually inform a viewer of the global andrelative contributions of different component of a time-seriesforecasting model. For example, an output signal (predicted value overtime) can be decomposed into a plurality of sub-signals (one for eachcomponent). The sub-signals can be displayed along with the outputsignal in a signal decomposition graph that has one uniform scale forall components. Furthermore, the decomposition process can determine theglobal contribution values of the different components over a horizon oftime or multiple horizons of time thereby providing a fullerunderstanding of the contribution of each component. The impact createdby each component can be visually represented using graphical elements(e.g., bar graphs, etc.) and displayed along with the decompositiongraph.

According to various embodiments, the system can estimate a global andrelative contribution value of each component to the predicted outputvalue (forecasted value) from an instant decomposition of a time-seriesforecasting model. Here, a contributive percentage can be assigned toeach component (e.g., trend, cycles, fluctuations, residuals, etc.) withrespect to the overall predictive output signal. The algorithm used todetermine the contribution value may be an agnostic method that isderived from a proven mathematical foundation, a Shapley value. Thecontribution of each component can be determined from a plurality ofunits of time (e.g., a horizon) may adding together an absolute value ofthe component at each time increment. Furthermore, the method can beapplied consistently on both additive and multiplicative decompositions.In some embodiments, a multiplicative decomposition can be convertedinto an additive decomposition using a conversion function. By using anabsolute value, the system can ignore the direction of the contributionof a component (e.g., positive or negative) and instead consider onlythe amount of change at each time increment.

FIG. 1 illustrates a process 100 of executing a machine learning model122 and a decomposition application 124 in accordance with an exampleembodiment. Referring to FIG. 1, a host platform 120, for example, acloud platform, a web server, a user device, a database, or the like,may execute a machine learning model 122. As an example, the machinelearning model 122 may be a time-series forecasting model such as ETS,ARIMA, or the like. Time-series data 110 may be input to the machinelearning model 122. As an example, the time-series data 110 may includeany kind of time-series data such as sales data, quantity data, sensordata (e.g., Internet of Things, etc.), and the like, which dynamicallychanges over time.

The host platform 120 may execute an iteration of the machine learningmodel 122 on the input data 110 to generate a data point of a predictedoutput signal. The predicted data point may include a measure of thevalue being predicted at a point in time, for example, a predicted salesquantity of apples for a particular day. The execution of the machinelearning model 122 may be iteratively performed to generate a pluralityof forecasted data points such as shown in the example of thetime-series forecasting signal 210 shown in FIG. 2A. Here, eachforecasted output (e.g., based on an execution of the machine learningmodel 122) creates a new data point of the time-series forecastingsignal 210 at a next increment of time on the graph. The forecasts mayinclude forecasts for multiple intervals of time equal to a horizonvalue (h) which may be a predetermined number that is set by a user orby a software program. As an example, the horizon may include threeintervals, four intervals, five intervals, six intervals, sevenintervals, and the like. Continuing with the example of the sales ofapples, a horizon may be a week (7 days) and the predicted output valuemay include seven data points for the seven days of a week.

The time series forecasting signal 210 in FIG. 2A includes acombination/contribution from a plurality of different sub componentsrepresented by sub component signals 220, 230, and 240 shown in FIG. 2B.In this example, FIG. 2B illustrates a trend component 220, a cyclicalcomponent 230, and an influencer component 240. In the example of FIGS.2A and 2B, the scale of each of the component signals 220, 230, and 240differs from the scale of the time-series output signal 210. Forexample, the scale of the trend component signal 220 slightly differsfrom the scale of the time-series output signal 210. However, the scalesof the cyclical component signal 230 and the influencer component signal240 greatly differ from the scale of the time-series output signal. Inparticular, the influencer component signal varies from 1.1 to 0.9 whilethe time-series output signal varies from 600 to 100. Thus, it can bedifficult to visualize the impact of the different sub-component signalson the overall predicted time-series output signal 210 in FIG. 2A.

Next, the host platform 120 may execute a decomposition application 124on the predicted output signal of the machine learning model 122. Thedecomposition application 124 may identify individual contributions ofeach component from among a plurality of components of the time-seriesforecasting model on the overall predicted output value output by thetime-series forecasting model. Examples of the components include atrend component, a cyclical component (e.g., seasonal, weekly, etc.), aninfluencer component, a fluctuation component, a residual component, andthe like. The trend component represents the general pattern of thetime-series forecasting output value over time. The cyclical componentmay be a recurring pattern within the predictive output signal thatrepeats itself every predetermined number of intervals (e.g., everyweek, every day, every month, etc.) The influencer component may berandom (e.g., not predictable) and may not have logic associatedtherewith. For example, the influencer component may result from theoccurrence of critical events, changes in the market, changes in price,and the like.

The decomposition application 124 may display a graph of the predictedoutput signal graphed over time as well as graphs of the sub-signals(components) over time such as shown in the example of FIG. 3A and FIG.3B.

FIG. 3A illustrates a graph 300A displaying different component signalsof a time-series forecasting model in accordance with an exampleembodiment. Referring to FIG. 3A, a time-series forecasting model maypredict an output signal 310 shown on the graph 300A. The graph 300A maybe output via a user interface that is displayed in a web page, a mobileapplication, a web application, and the like. For example, the graph300A may be output by the decomposition application 124 shown in FIG. 1.In this example, the output value that is being predicted is sales of anitem in US dollars. The sales value represents the y-axis value of thepredicted output and an increment of time (e.g., days) represents thex-axis value. As an example, the time-series forecasting model F(t) maybe represented as follows for the additive variant:

F(t)=Trend(t)+Cyclical(t)+Influencer(t)+Residuals(t) . . .

Here, the model includes a plurality of components (sub components) thatcontribute to the overall predicted output value including a trendcomponent, a cyclical component, and an influencer component. Othercomponents may include residual, fluctuation, random, etc. Eachcomponent may provide a partial contribution to the overall predictedoutput value at each increment of time.

In FIG. 3A, the trend component is represented by signal 312 and has ageneral pattern that is roughly the same scale as the predicted outputsignal 310. The cyclical component is represented by signal 314 and hasa recurring pattern that occurs every predetermined number of sequencesof time. The influencer component is represented by signal 316 andincludes a random pattern that is not based on logic. Here, theinfluencer component may represent changes in the market, alerts orother breaks in normalcy of the data, price fluctuations, and the like.There are many possible influence components. Furthermore, the residualsfrom the timer-series forecasting model are represented by signal 318.The graph 300A differentiates from the different signals using brokenline graphs. But it should be appreciated that colored lines may be usedinstead of broken line graphs, or any other visual differentiators suchas changes to the width, etc. of the lines.

In this example, each of the cyclical component signal 314, theinfluencer component signal 316, and the residual component signal 318have a different scale than the predicted output signal 310. However,the graph 300A is constructed by the system described herein such thateach of the different signals (e.g., predicted output signal 310, trendsignal 312, cyclical component signal 314, influencer component signal316, and residual component signal 318 are displayed on a common axishave one scale.

FIG. 3B illustrates a process 300B of displaying global impact values ofthe different component signals of the time-series forecasting model inaccordance with an example embodiment. Referring to FIG. 3B, in additionto displaying the graph 300A in FIG. 3A, the application (e.g.,decomposition application) described herein may generate and output animpact window 330 which provides a graphicalvisualization/representation of the impact (contribution) of eachcomponent on the overall predicted output signal 310. In this example,the impact window 330 includes identifiers of the components which inthis example is the names of the components (e.g., trend, cycle,influencers, residuals, and fluctuations). Each identifier is displayednext to its corresponding line graph. Furthermore, the plurality of bargraphs are aligned with and displayed next to the plurality ofidentifiers. Here, each identifier is paired with its corresponding bargraph. In addition, a percentage value which represents the globalcontribution of a component may also be displayed next to or inside ofthe bar graph.

According to various embodiments, the decomposition application may alsogenerate a visualization of the (global contribution value) of eachcomponent. In this example, the visualizations are bar graphs, but theembodiments are not limited thereto. It should be appreciated that anyshapes may be used such as lines, rectangles, squares, circles, etc., ormultiple shapes arranged next to each other may be used. The size of thebar graph represents the contribution value in percentage. Here, thetrend component signal 312 has the greatest contribution to thepredicted output value signal 310. Therefore, the bar graph thatcorresponds to the trend component is the largest/widest bar graph inthe group shown in the impact window 330 thereby enabling a viewer toquickly identify the component with the greatest impact.

The cyclical component signal 314 has the second greatest impact on thepredicted output value signal 310. Accordingly, the cyclical component314 (represented by identifier 331 in the impact window 330) has acorresponding bar graph 334 that is the second largest among the bargraphs in the impact window 330. Here, each bar graph is displayedadjacent and in alignment with its corresponding identifier. In otherwords, the bar graph 334 that represents the global contribution valueof the cyclical component signal 314, is displayed adjacent to theidentifier 331 of the cyclical component signal 314 in the impact window330.

In some embodiments, the impact window 330 may be an interactive windowthat a user can interact with using a pointing device (e.g., a mouse, afinger, a pointer, a keyboard, etc.) Here, the user has moved a cursoronto the identifier 331 and selected it causing identifiers ofsub-components of the cyclical component signal to be displayedunderneath. Here, the sub-components of the cyclical component signal314 include a yearly signal component and a weekly signal componentrepresented with identifiers 332 and 333, respectively, in the impactwindow 330. Each sub-component may have a correspond bar graph (bargraphs 335 and 336) representing the global contribution values of therespective sub-component signals on the predicted output signal value310.

FIG. 4A illustrates a process 400A of generating a decomposition tablefor global contribution value determination in accordance with exampleembodiments. Referring to FIG. 4A, the time-series forecasting model maybe an additive algorithm 402 or a multiplicative algorithm 404. Ineither case, additive decomposition may be performed. For example, for atime-series forecasting model that includes a multiplicative algorithmsuch as algorithm 404, the multiplicative algorithm can be reformulatedinto an additive algorithm. Below is an example of such a conversion.Such conversion is useful as instant additive decomposition is aprerequisite of the proposed method to compute the relative globalcontribution of each component i.

F(t)=Trend(t)+((Cyclical(t)−1)*Trend(t))+((Influencer(t)−1)*Cyclical(t)*Trend(t)). . .

Each additive component should depend only on the leftmostmultiplicative component assuming that the multiplicative decompositionhas an order: Then Cyclical then Influencer and so on. In aboveexpression, the additive component related to the multiplicativeCyclical component is ((Cyclical(t)−1)*Trend(t)) and the additivecomponent related to the multiplicative Influencer component is((Influencer (t)−1)*Cyclical(t)*Trend(t)).

By converting the multiplicative algorithm into an additive algorithm,additive decomposition can be performed for each time increment.

The global contribution can be determined by generating a data structure(decomposition table 410) which is used to store instant contributionvalues of each component over a plurality of time increments referred toas a horizon. That is, the application can determine an additivedecomposition for each component of the time-series forecasting signalto determine a global contribution value of each component for thepredicted output value. The horizon may represent a subset of time inthe predicted output signal. As an example, the predicted output signalmay provide 31 days of data with 31 data points graphed over 31 pointsin time. Here, the horizon may be seven days which is a subset of the 31days of the predicted output signal. Furthermore, multiple horizons(subsets) may exist in the predicted output signal. For example, days1-7 may correspond to a first horizon, days 8-14 may correspond to asecond horizon, days 15-21 may correspond to a third horizon, etc.

The construct the decomposition table 410, the application may insert orotherwise add values of each component at each increment of time for apredetermined number of increments of time (horizon). In this example,the horizon is four increments of time. At each increment, the componentsignal values change by increasing (+) or decreasing (−). For example,during a first increment of time, the trend component contribution valueis three (3). During the second increment of time, the trend componentcontribution value decreases by two (−2). During the third increment oftime, the trend component contribution value decrease by one (−). Eachvalue (change in the component signal) from increment to increment maybe stored in the table. Here, each component has its own dedicatedcolumn in the table 410. It should also be appreciated that differentdata structures may be used besides a table such as an array, adocument, a spreadsheet, a file, or the like.

In the decomposition table 410, each row represents a different timeincrement with the last row (bottom row) representing a total orsummation of values for the horizon. To generate the summation, theapplication uses absolute values and ignores the (+) or (−) associatedwith the individual component values. In other words, the application isonly interested in the amount of change in the signal and not thedirection (i.e., negative or positive). Therefore, a sum value 412 ofthe trend component signal for the horizon is ten (10), a sum value 414of the cyclical component signal is six (6), and a sum value 416 of theinfluencer component signal is five (5). The total contribution value418 of all signals is generated by adding the sum values 412, 414, and416. In this example, the total contribution value is twenty-one (21).

To determine the global contribution value of each of the differentcomponents, the application can divide each of the sum values 412, 414,and 416, by the total contribution value 418 to arrive at the globalcontribution values 422, 424, and 426. Here, the global contributionvalues 422, 424, and 426, may be stored in a column of a contributiontable 420. The contribution table 420 may also include another columnwith identifiers of the components displayed therein. Any of thedecomposition table 410 and the contribution table 420 may be output viaa user interface (for display) on a screen of a user device. As anotherexample, the global contribution values 422, 424, and 426 may be outputby themselves or as part of an application template.

FIG. 4B illustrates a process 400B of determining multi-dimensionalglobal contribution values for the plurality of component signals inaccordance with an example embodiment. In order to provide a more robustglobal contribution determination, the application may compute severaldecompositions for several horizons of time (e.g., subsets of datapoints). In this example, the horizons may include sequential andnon-overlapping intervals of time. As noted above, the first horizon maybe time units 1-7 while the second horizon may be time units 8-14. Here,the application may determine global contribution values using for aplurality of horizons by iteratively perform the process 400A describedin FIG. 4A for different horizons.

In the example of FIG. 4B, global contribution values of the threecomponent signals are determined for four iterations of time (fourhorizons) and are stored in a contribution table 430. Here, theidentifier (I₁) represents the first iteration, the identifier (I₂)represents the second iteration, and so on. Here, the application maydetermine multi-dimensional global contribution values 432, 434, and 436for the components by adding the global contribution values together anddividing by the number of intervals. The multi-dimensional globalcontribution values may be output for display.

FIG. 5 illustrates a method 500 a method of determining globalcontribution values of a plurality of components of a time-seriesforecasting model in accordance with an example embodiment. For example,the method 500 may be executed by a database node, a cloud platform, aserver, a computing system (user device), a combination ofdevices/nodes, or the like. Referring to FIG. 5, in 510, the method mayinclude iteratively predicting an output signal of a time-series datavalue via execution of a time-series machine learning model on inputdata. For example, the host platform may repeatedly execute atime-series machine learning model on input data to generate thepredicted output signal. As a result of each iteration, the machinelearning model may output one or more predicted data points of a datavalue in the future. The predicted output signal may be graphed overtime with each predicted data point being associated with a timeincrement on the graph.

In 520, the method may include decomposing the predicted output signalinto a plurality of component signals corresponding to a plurality ofcomponents of the time-series machine learning model, respectively. Forexample, the component signals may include one or more of a trendcomponent, a cyclical component, an influencer component (e.g., randomfluctuation component, etc.), a residual component, and the like. Eachcomponent signal may provide a partial contribution to the predictedoutput signal. The component signals may have different patterns,different scales, different values, and the like, with respect to eachother. Here, the summation of the plurality of component signals at apoint in time may be equal to the overall predicted output signal of theforecasting model at the point in time.

In 530, the method may include determining a plurality of global valuescorresponding to the plurality components signals, respectively, for afirst subset of the predicted output signal, where a global value isdetermined based on an absolute value of a respective component signalwithin the first subset of the predicted output signal, and in 540, themethod may include displaying the plurality of global values via a userinterface. The first subset may be a first horizon within the predictedoutput signal. A horizon may be any desired size of time increments suchas two or more data increments. The global values may correspond to thecontribution values that each component signal provides to the predictedoutput signal. The global value may be a percentage between 0% and1000%, where 100% represents the entire predicted output signal.

In some embodiments, the determining may include, for each componentsignal, identifying a plurality of partial values of the respectivecomponent signal within the first subset of the predicted output signal,and storing the plurality of identified partial values in a plurality ofcells of a respective column in a data structure. In this example, thedetermining may further include converting the plurality of partialvalues of the component signal into a plurality of absolute partialvalues and determining a global value for the component signal based onthe plurality of absolute partial values.

In some embodiments, the method may further include determining aplurality of additional global values corresponding to the pluralitycomponent signals, respectively, for a second subset of the predictedoutput signal that is different than the first subset of the predictedoutput signal. In some embodiments, the method may further includedetermining a plurality of multi-dimension global values for theplurality of component signals, respectively, based on the plurality ofglobal values of the first subset of the predicted output signal and theplurality of different global values of the second subset of thepredicted output signal.

In some embodiments, the method may further include constructing aplurality of bars corresponding to the plurality of global values of theplurality of component signals, respectively, and outputting theplurality of bars in a vertical arrangement via the user interface. Insome embodiments, the decomposing may include decomposing the predictedoutput signal into the plurality of component signals based on additivedecomposition. In some embodiments, the decomposing may further includeconverting a multiplicative time-series algorithm into an additivetime-series algorithm, prior to decomposition of the predicted outputsignal.

FIG. 6 illustrates a computing system 600 that may be used in any of themethods and processes described herein, in accordance with an exampleembodiment. For example, the computing system 600 may be a databasenode, a server, a cloud platform, or the like. In some embodiments, thecomputing system 600 may be distributed across multiple computingdevices such as multiple database nodes. Referring to FIG. 6, thecomputing system 600 includes a network interface 610, a processor 620,an input/output 630, and a storage device 640 such as an in-memorystorage, and the like. Although not shown in FIG. 6, the computingsystem 600 may also include or be electronically connected to othercomponents such as a display, an input unit(s), a receiver, atransmitter, a persistent disk, and the like. The processor 620 maycontrol the other components of the computing system 600.

The network interface 610 may transmit and receive data over a networksuch as the Internet, a private network, a public network, an enterprisenetwork, and the like. The network interface 610 may be a wirelessinterface, a wired interface, or a combination thereof. The processor620 may include one or more processing devices each including one ormore processing cores. In some examples, the processor 620 is amulticore processor or a plurality of multicore processors. Also, theprocessor 620 may be fixed or it may be reconfigurable. The input/output630 may include an interface, a port, a cable, a bus, a board, a wire,and the like, for inputting and outputting data to and from thecomputing system 600. For example, data may be output to an embeddeddisplay of the computing system 600, an externally connected display, adisplay connected to the cloud, another device, and the like. Thenetwork interface 610, the input/output 630, the storage 640, or acombination thereof, may interact with applications executing on otherdevices.

The storage device 640 is not limited to a particular storage device andmay include any known memory device such as RAM, ROM, hard disk, and thelike, and may or may not be included within a database system, a cloudenvironment, a web server, or the like. The storage 640 may storesoftware modules or other instructions which can be executed by theprocessor 620 to perform the method shown in FIG. 5. According tovarious embodiments, the storage 640 may include a data store having aplurality of tables, records, partitions and sub-partitions. The storage640 may be used to store database records, documents, entries, and thelike.

As will be appreciated based on the foregoing specification, theabove-described examples of the disclosure may be implemented usingcomputer programming or engineering techniques including computersoftware, firmware, hardware or any combination or subset thereof. Anysuch resulting program, having computer-readable code, may be embodiedor provided within one or more non-transitory computer-readable media,thereby making a computer program product, i.e., an article ofmanufacture, according to the discussed examples of the disclosure. Forexample, the non-transitory computer-readable media may be, but is notlimited to, a fixed drive, diskette, optical disk, magnetic tape, flashmemory, external drive, semiconductor memory such as read-only memory(ROM), random-access memory (RAM), and/or any other non-transitorytransmitting and/or receiving medium such as the Internet, cloudstorage, the Internet of Things (IoT), or other communication network orlink. The article of manufacture containing the computer code may bemade and/or used by executing the code directly from one medium, bycopying the code from one medium to another medium, or by transmittingthe code over a network.

The computer programs (also referred to as programs, software, softwareapplications, “apps”, or code) may include machine instructions for aprogrammable processor, and may be implemented in a high-levelprocedural and/or object-oriented programming language, and/or inassembly/machine language. As used herein, the terms “machine-readablemedium” and “computer-readable medium” refer to any computer programproduct, apparatus, cloud storage, internet of things, and/or device(e.g., magnetic discs, optical disks, memory, programmable logic devices(PLDs)) used to provide machine instructions and/or data to aprogrammable processor, including a machine-readable medium thatreceives machine instructions as a machine-readable signal. The“machine-readable medium” and “computer-readable medium,” however, donot include transitory signals. The term “machine-readable signal”refers to any signal that may be used to provide machine instructionsand/or any other kind of data to a programmable processor.

The above descriptions and illustrations of processes herein should notbe considered to imply a fixed order for performing the process steps.Rather, the process steps may be performed in any order that ispracticable, including simultaneous performance of at least some steps.Although the disclosure has been described in connection with specificexamples, it should be understood that various changes, substitutions,and alterations apparent to those skilled in the art can be made to thedisclosed embodiments without departing from the spirit and scope of thedisclosure as set forth in the appended claims.

What is claimed is:
 1. A computing system comprising: a hardwareprocessor configured to: iteratively predict an output signal of atime-series data value via execution of a time-series machine learningmodel on input data, decompose the predicted output signal into aplurality of component signals corresponding to a plurality ofcomponents of the time-series machine learning model, respectively,determine a plurality of global values corresponding to the pluralitycomponents signals, respectively, for a first subset of the predictedoutput signal, where a global value is determined based on an absolutevalue of a respective component signal within the first subset of thepredicted output signal, and display the plurality of global values viaa user interface.
 2. The computing system of claim 1, wherein, for eachcomponent signal, the hardware processor is configured to identify aplurality of partial values of the respective component signal withinthe first subset of the predicted output signal, and store the pluralityof identified partial values in a plurality of cells of a respectivecolumn in a data structure.
 3. The computing system of claim 2, whereinthe hardware processor is configured to convert the plurality of partialvalues of the component signal into a plurality of absolute partialvalues and determine a global value for the component signal based onthe plurality of absolute partial values.
 4. The computing system ofclaim 1, wherein the plurality of component signals comprise a trendsignal, a cyclic signal, and a fluctuation signal within the time-seriesmachine learning model.
 5. The computing system of claim 1, wherein thehardware processor is further configured to determine a plurality ofadditional global values corresponding to the plurality componentsignals, respectively, for a second subset of the predicted outputsignal that is different than the first subset of the predicted outputsignal.
 6. The computing system of claim 5, wherein the hardwareprocessor is further configured to determine a plurality ofmulti-dimension global values for the plurality of component signals,respectively, based on the plurality of global values of the firstsubset of the predicted output signal and the plurality of differentglobal values of the second subset of the predicted output signal. 7.The computing system of claim 5, wherein the first subset of thepredicted output signal and the second subset of the predicted outputsignal are non-overlapping.
 8. The computing system of claim 1, whereinthe hardware processor is configured to construct a plurality of barscorresponding to global values of the plurality of component signals,respectively, and output the plurality of bars in a vertical arrangementvia the user interface.
 9. The computing system of claim 1, wherein thehardware processor is configured to decompose the predicted outputsignal into the plurality of component signals based on additivedecomposition.
 10. The computing system of claim 9, wherein the hardwareprocessor is configured to convert a multiplicative time-seriesalgorithm into an additive time-series algorithm, prior to decompositionof the predicted output signal.
 11. A method comprising: iterativelypredicting an output signal of a time-series data value via execution ofa time-series machine learning model on input data; decomposing thepredicted output signal into a plurality of component signalscorresponding to a plurality of components of the time-series machinelearning model, respectively; determining a plurality of global valuescorresponding to the plurality components signals, respectively, for afirst subset of the predicted output signal, where a global value isdetermined based on an absolute value of a respective component signalwithin the first subset of the predicted output signal; and displayingthe plurality of global values via a user interface.
 12. The method ofclaim 11, wherein the determining comprises, for each component signal,identifying a plurality of partial values of the respective componentsignal within the first subset of the predicted output signal, andstoring the plurality of identified partial values in a plurality ofcells of a respective column in a data structure.
 13. The method ofclaim 12, wherein the determining further comprises converting theplurality of partial values of the component signal into a plurality ofabsolute partial values and determining a global value for the componentsignal based on the plurality of absolute partial values.
 14. The methodof claim 11, wherein the plurality of component signals comprise a trendsignal, a cyclic signal, and a fluctuation signal within the time-seriesmachine learning model.
 15. The method of claim 11, further comprisingdetermining a plurality of additional global values corresponding to theplurality component signals, respectively, for a second subset of thepredicted output signal that is different than the first subset of thepredicted output signal.
 16. The method of claim 15, further comprisingdetermining a plurality of multi-dimension global values for theplurality of component signals, respectively, based on the plurality ofglobal values of the first subset of the predicted output signal and theplurality of different global values of the second subset of thepredicted output signal.
 17. The method of claim 11, wherein the methodfurther comprises constructing a plurality of bars corresponding to theplurality of global values of the plurality of component signals,respectively, and outputting the plurality of bars in a verticalarrangement via the user interface.
 18. The method of claim 11, whereinthe decomposing comprises decomposing the predicted output signal intothe plurality of component signals based on additive decomposition. 19.The method of claim 18, wherein the decomposing further comprisesconverting a multiplicative time-series algorithm into an additivetime-series algorithm, prior to decomposition of the predicted outputsignal.
 20. A non-transitory computer-readable medium comprising programinstructions which when executed by a hardware processor cause thehardware processor to perform a method comprising: iterativelypredicting an output signal of a time-series data value via execution ofa time-series machine learning model on input data; decomposing thepredicted output signal into a plurality of component signalscorresponding to a plurality of components of the time-series machinelearning model, respectively; determining a plurality of global valuescorresponding to the plurality components signals, respectively, for afirst subset of the predicted output signal, where a global value isdetermined based on an absolute value of a respective component signalwithin the first subset of the predicted output signal; and displayingthe plurality of global values via a user interface.